In order to produce images of the subsurface, geologists or geophysicists conventionally use acoustic transmitters placed, for example, at the surface. As shown in FIG. 1, the transmitters S (also called sources) transmit waves that are propagated in the subsurface and reflected on the surfaces of the layers thereof (reflectors). The acoustic waves reflected toward the surface are recorded as a function of time by receivers R. The signals recorded by the receivers are called seismic traces.
Various digital processing techniques are conventionally applied to these traces so as to improve the signal-to-noise ratio and facilitate their interpretation. These techniques include the migration operation, which consists of determining, for a plurality of surface positions P of coordinates (x, y), a collection of migrated traces bearing information on events that describe the subsurface in line with the surface position P (x, y). The migration can be applied before or after the stacking of the traces, and we refer to time migration or depth migration depending on whether the output traces are represented according to the time or the depth. In both cases, the repositioning of events is based on a model of the wave propagation velocity in the subsurface, i.e., a time-velocity model for the time migration or a depth-velocity model for the depth migration. The time- or depth-velocity model makes it possible to calculate the travel time between the source and receiver positions and the image point. The estimation of the time- or depth-velocity model is an important and difficult step in the seismic processing chain.
There are numerous ways of arranging the collections of traces migrated before stacking of the data. It is thus possible to group all of the traces in line with a surface position P (x, y) and constitute gathers of traces at a common image point called a CIP (Common Image Point) gather. Generally, these CIP gathers are organized according to the source-receiver distance (also called the offset distance) as shown in FIG. 2, but it is also possible to organize them according to the angles of reflection, the orientation of the source-receiver segment, slopes at the surface, the position of the sources and receivers, etc. The analysis of the migrated images obtained for these different classes is the basis for numerous seismic trace processing techniques. Thus, CIP gathers are very widely used for the interpretation of subterranean geological structures:
1) the stacking of the traces of the CIP gathers at a constant surface position gives a precise image of the structure of the subsurface,
2) the form of the events observed on the CIP gathers makes it possible to assess the quality of the velocity model used in the migration,
3) the amplitude of the events observed on the CIP gathers provides information on the mechanical characteristics of the formations encountered (AVO “Amplitude Versus Offset” studies).
Various techniques have thus been proposed for analyzing these CIP gathers. However, while precise analyses have been carried out in the case of the depth migration, they have not yet been reported in the case of time migration, of which the analysis is often affected by the assumptions of constant time velocity and/or of the absence of dip.